Copulas define statistical relationships between two (or more) random variables u and v in unity space. That is to say, both variables lie between zero and one, and both variables follow a uniform marginal probability density function.

The copula's joint density defines how the samples of u and v coincide, clustering more densely around regions of high probability density. Copulas also affect tail dependency: asymmetric copulas such as the Clayton and Gumbel copula enforce stronger correlations in the bivariate distribution's lower and upper tails, respectively.